Solve the Following Question.(4 Marks)

Question

Calculate mean deviation about median age distribution of 100 persons given below: Age 16-20 21-25 26-30 31-35 36-40 41-45 46-50 51-55 No. of persons 5 6 12 14 26 12 16 9

Accepted Answer

Converting the given data into continuous frequency distribution by subtrading $0.5$ from the lower limit and adding $0.5$ to the upper limit of each class interval.

Age	$x_i$	$f_i$	Comulativefrequency	$\|d_i\| = \|x_i - 38\|$	$f_i\|d_i\|$
$15.5-20.5$	$18$	$5$	$5$	$20$	$100$
$20.5-25.5$	$23$	$6$	$11$	$15$	$90$
$25.5-30.5$	$28$	$12$	$23$	$10$	$120$
$30.5-35.5$	$33$	$14$	$37$	$5$	$70$
$35.5-40.5$	$38$	$26$	$63$	$0$	$0$
$40.5-45.5$	$43$	$12$	$75$	$5$	$60$
$45.5-50.5$	$48$	$16$	$91$	$10$	$160$
$50.5-55.5$	$53$	$9$	$100$	$15$	$135$
		$\text{N}=\sum\text{f}_\text{i}=100$			$\sum\text{f}_\text{i}\|\text{d}_\text{i}\|=735$

clearly, $N = 100$
$\Rightarrow\frac{\text{N}}{2}=50.$
Cumulative frequency is just greater than
$\frac{\text{N}}{2}$ is $63$ and the corresponding class is $35.5 - 40.5.$
$l = 35.5, f = 26, h = 5, F = 37$
Therefore, $\text{Median}=\text{l}+\frac{\frac{\text{N}}{2}-\text{F}}{\text{f}}\times\text{h}=35.5+\frac{50-37}{26}\times5=38$
$\text{M.D}=\frac{1}{\text{N}}\sum\text{f}_\text{i}|\text{d}_\text{i}|=\frac{735}{100}=7.35$

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Age	$16-20$	$21-25$	$26-30$	$31-35$	$36-40$	$41-45$	$46-50$	$51-55$
No. of persons	$5$	$6$	$12$	$14$	$26$	$12$	$16$	$9$

Statistics — Maths STD 11 Science — Question

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